Advanced search
Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 81, 2009 - Issue 3-4: Stochastic Analysis
Submit an article Journal homepage
49
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Evolution equation associated to the powers of the quantum Gross Laplacian

Soumaya Gheryani Department of Mathematics, University of Tunis El Manar Tunisia, Tunis, Tunisia
,
Samah Horrigue Department of Mathematics, University of Tunis El Manar Tunisia, Tunis, Tunisia
&
Habib Ouerdiane Department of Mathematics, University of Tunis El Manar Tunisia, Tunis, TunisiaCorrespondence[email protected]
Pages 355-366 | Received 10 May 2008, Accepted 26 Jul 2008, Published online: 23 Jul 2009

References

  • Barhoumi , A. , Kuo , H.H. and Ouerdiane , H. 2006 . Generalized Gross heat equation with noises . Soochow J. Math. , 32 ( 1 ) : 113 – 125 .
  • Ben Chrouda , M. and Ouerdiane , H. 2002 . Algebra of operators on holomorphic functions and applications . J. Math. Phys. Anal. Geom. , 5 : 65 – 76 .
  • Ben Chrouda , M. , El Oued , M. and Ouerdiane , H. 2002 . Convolution calculus and applications to stochastic differentntial equations . Soochow J. Math. , 28 : 375 – 388 .
  • Chung , D.M. and Ji , U.C. 1999 . Some Cauchy problems in white noise analysis and associated semigroups of operators . Stoch. Anal. Appl. , 17 ( 1 ) : 1 – 22 .
  • Gannoun , R. , Hachaichi , R. , Ouerdiane , H. and Rezgui , A. 2000 . Un théorème de dualité entre espace de fonctions Holomorphes à croissance exponentielle . J. Funct. Anal. , 171 : 1 – 14 .
  • Gheryani , S. , Kuo , H.-H. and Ouerdiane , H. 2007 . Evolution equation associated with the power of the Gross Laplacian . Adv. Theor. Appl. Math. , 2 ( 1 ) : 41 – 50 .
  • Gross , L. 1967 . Potential theory on Hilbert space . J. Funct. Anal. , 1 : 123 – 181 .
  • Hida , T. , Obata , N. and Saitô , K. 1992 . Infinite-dimensional rotations and Laplacians in terms of white noise calculus . Nagoya Math. J. , 128 : 65 – 93 .
  • Hida , T. , Kuo , H.H. , Potthoff , J. and Streit , L. 1993 . White Noise. An Infinite Dimensional Calculus , Dordrecht : Kluwer Academic Publishers .
  • S. Horrigue and H. Ouerdiane, Gross Laplacian acting on operators, Acta Appl. Math. 105 (2009), pp. 227–239
  • Horrigue , S. and Ouerdiane , H. (2009) . Quantum Gross Laplacian and applications . Acta Appl. Math. , DOI: 10.1007/s10440-008-9401-5
  • Ji , U.C. , Obata , N. and Ouerdiane , H. 2002 . Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition . World Sci. , 5 ( 3 ) : 395 – 407 .
  • Kuo , H.H. 1986 . On Laplacian operators of generalized Brownian functionals . Lect. Notes Math. , 1203 : 119 – 128 .
  • Obata , N. 1994 . White noise calculus and fock spaces , Lect. Notes in Math Vol. 1577 ,
  • Ouerdiane , H. 1995 . Noyaux et symboles d'opérateurs sur des fonctionnelles analytiques gaussiennes . Japan. J. Math. , 21 : 223 – 234 .
  • Piech , M.A. 1970 . A fundamental solution of the parabolic equation on Hilbert space II. The semigroup property . Trans. Amer. Math. Soc. , 150 : 257 – 286 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Supercharge Your Next Research Paper: Research and write your next paper with Jenni AI.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.